It is well known to obtain three-dimensional arrays of data representing one or more physical properties at regular grid positions within the interior of solid bodies. Such data can be obtained by non-intrusive methods such as computed axial tomographic (CAT) x-ray scanning systems, by nuclear magnetic resonance (NMR) imaging systems, or by other non-intrusive mechanisms such as ultrasound, positron emission tomography (PET), emission computed tomography (ECT) and multimodality imaging (MMI). Each of these techniques produces a planar, grid-like array of values for each of a succession of slices of the solid object, thus providing a three-dimensional array of such values. Typically, the solid object is a human body or a portion thereof, although the method is equally applicable to other natural or artificial bodies. In the case of CAT scanning, the physical value would be the coefficient of x-ray absorption. For NMR imaging, the physical value would be the spin-spin or the spin-lattice relaxation time. In any event, the measured physical values reflect the variations in composition, density or surface characteristics of the underlying physical structures. Such a three-dimensional data array typically consists of a plurality of sets of three-dimensional (x, y, z) coordinates distributed at regular positions in a cubic or parallelepiped lattice within the body, and at least one value (V.sub.xyz) of the physical property being associated with each respective one of the coordinate positions. Each cubically adjacent set of eight such positions defines a cubic volume called a "voxel" with a physical property value being specified for each of the eight voxel vertices.
It is likewise known to utilize such three-dimensional arrays of interior physical values to generate visual images of the interior structures within the body. In the case of the human body, the visual images thus produced can be used for medical purposes such as diagnostics or for the planning of surgical procedures. In order to display two-dimensional images of such three-dimensional interior structures, however, it is necessary to locate the position of the surface of such structure within the array of physical values. This is accomplished by comparing the array values to a single threshold value, or to a range of threshold values, corresponding to the physical property values associated with that surface. Bones or any other tissue, for example, can be characterized by a known range of density values to which the array values can be compared. Once the surface location is determined, this surface must be shaded so as to give the human eye the correct impression of the shape and disposition of that surface when it is displayed on a two-dimensional display device. To provide such shading, the angular direction of a vector normal or orthogonal to the surface at each point on the surface is compared to the viewing angle of the observer. The intensity of shading can then be adjusted so as to be proportional to the difference between these angles. Such angular difference information can also be used to control the colors incorporated in the displayed images, thus providing yet another visual clue to the surface disposition. Normal vectors with components directed away from the viewing angle can be ignored since the associated surfaces are hidden from view.
One method for approximating the surface of an internal structure is the so called "marching cubes" method, disclosed by H. E. Cline et al. U.S. Pat. No. 4,710,876, granted Dec. 1, 1987, and assigned to applicants' assignee. In this method, the surface segment intersecting a voxel is approximated by one of a limited number of standardized plane polygonal surfaces intersecting the voxel. One particular standardized surface is selected by a vector representing the binary differences between the threshold value and the eight voxel vertex values. The surface-to-voxel intersection coordinates, as well as the normal vector, for each such standardized polygonal surface set can then be calculated or obtained by table look-up techniques. The final surface is assembled as a mosaic, using all the standardized polygons as tessera or tiles. Appropriate intensity values derived from the normal vector angles can be displayed immediately for viewing, or stored for later display. H. E. Cline et al. U.S. Pat. No. 4,729,098, granted Mar. 1, 1988, and also assigned to applicants' assignee, shows a variation of the marching cubes method using nonlinear interpolation to locate more accurately the coordinates of the tessellated standardized polygons.
Another method for approximating the surface of an internal structure is the so-called "dividing cubes" method, disclosed in H. E. Cline et al. U.S. Pat. No. 4,7l9,585, granted Jan. 12, 1988, and also assigned to applicants assignee. In this method, the values at the vertices of the voxel are used to interpolate, in three dimensions, values at regularly positioned intra-voxel sub-grid locations. These interpolated sub-grid values can then be used to locate the surface position more precisely and to calculate the normal vector more accurately.
In order to distinguish between different internal structures with the same or similar physical property values, W. E. Lorensen et al. U.S. Pat. No. 4,751,543, granted June 14, 1988, and likewise assigned to applicants' assignee, discloses a technique for labeling surfaces with similar property values and using adjacency criteria with respect to a "seed" location in the particular structure of interest to segregate the desired surface from all of the labeled surfaces. The copending application of H. E. Cline et al., U.S. Pat. No. 4,791,567, filed Sept. 15, 1986, also assigned to applicants' assignee, discloses another technique of segregating similar structures by determining connectivity from adjacency information. U.S. Pat. No. 4,821,213, filed Dec. 19, 1986, for H. E. Cline et al., and also assigned to applicants' assignee, discloses yet another technique for differentiating internal structures in which a linear pass is made through the data array to locate and label all of the different structures along the scan line by counting structure interfaces.
The generation of surface locations and normal vectors for three-dimensional solid objects such as bones is significantly speeded up by performing these two determinations in parallel. As shown in the copending application H. E. Cline et al., U.S. Pat. No. 4,821,213filed Dec. 19, 1986, and assigned to applicants' assignee, normal vectors are generated from "near neighbor" values in one of two parallel processing paths. The boundaries of the extended three-dimensional structure are simultaneously located in a parallel processing path by comparisons with one or more different threshold values representing one or more differential structural interfaces in the body, thereby to label the extended structure.
Thus it is known to use a single array of values of a physical property within the interior of a solid body to generate perspective images of arbitrarily selected internal structures within the body, seen as if viewed from arbitrarily chosen viewing angles, all by manipulating the selfsame single array of values. It is however, also desirable to view the solid body in cross section in order to see, not only the three-dimensional internal structures, but also to see the detailed spatial relationships between the different internal structures. These spatial relationships are particularly important for planning surgical procedures which impact on a plurality of the internal structures and which require a detailed foreknowledge of interstructural relationships. Organ transplants, for example, require detailed information concerning the size and geometry of the internal cavity into which the organ is to be inserted as well as the disposition of the neighboring organs.
While a simple display of one slice of the three-dimensional data will provide a cross-sectional view of the solid body, the view thus obtained may be inappropriate for the particular use intended. A preferred cross-sectional viewing plane which is orthogonal to structural interfaces may, for example, lie at some oblique angle to the orientation of the data acquisition slices. In that case, detailed and accurate cross-sectional views are not so readily obtained. Moreover, the need for real time, interactive generation of such images to support ongoing medical or surgical procedures is not readily met by the techniques available to the prior art.
Accordingly, one object of the invention is to provide an interactive method and apparatus for displaying two-dimensional cross-sectional images of a three-dimensional body.
Another object of the invention is to provide a system for displaying a three-dimensional array of physical values in a two-dimensional cross section taken in a selectable viewing plane.
Another object of the invention is to provide a system for displaying, with controllable pixel density, two-dimensional cross-sectional images of a three-dimensional body.
Another object of the invention is to provide a system for displaying in real time, with selectable enlargement capability, two-dimensional cross-sectional images of a three-dimensional body.